Infimal convolution, c-subdifferentiability, and Fenchel duality in evenly convex optimization

  1. M.D. Fajardo 1
  2. J. Vicente-Pérez 1
  3. M.M.L. Rodríguez 1
  1. 1 Universidad de Alicante, España
Revue:
Top

ISSN: 1863-8279,  1134-5764

Année de publication: 2012

Volumen: 20

Número: 2

Pages: 375-396

Type: Article

DOI: 10.1007/S11750-011-0208-6 SCOPUS: 2-s2.0-84864147529 DIALNET GOOGLE SCHOLAR

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Résumé

In this paper we deal with strong Fenchel duality for infinite-dimensional optimization problems where both feasible set and objective function are evenly convex. To this aim, via perturbation approach, a conjugation scheme for evenly convex functions, based on generalized convex conjugation, is used. The key is to extend some well-known results from convex analysis, involving the sum of the epigraphs of two conjugate functions, the infimal convolution and the sum formula of ε-subdifferentials for lower semicontinuous convex functions, to this more general framework.

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Information sur le financement

J. Vicente-Pérez has been supported by FPI Program of MICINN of Spain, Grant BES-2006-14041. M.D. Fajardo and M.M.L. Rodríguez have been supported by MICINN of Spain and FEDER of EU, Grant MTM2008-06695-C03-01.

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